This disclosure is related to the field of acoustic imaging of the Earth's subsurface. More specifically, the disclosure relates to methods for acquiring and processing acoustic signals from an array of sensors deployed above an area of the subsurface to be imaged.
Guigné et al. (U.S. Pat. No. 7,830,748) discloses a method for acoustic imaging of the Earth's subsurface using a fixed position seismic sensor array and beam steering for seismic surveying at higher lateral and vertical resolutions than currently possible with conventional 3D reflection seismic surveys. The method of disclosed in the '748 patent is based on a multiple line sensor array with a plurality of select seismic sensors having “dense” sensor spacing of adjacent sensors, i.e., no greater than ½ wavelength of the detected acoustic energy, to eliminate spatial aliasing of received signals at all wavelengths of interest. The method and system disclosed therein includes an array of broadband sources of acoustic energy capable of low order of transmit beam steering, a stationary source-receiver geometry to facilitate a plurality of source activations and common-receiver (i.e., vertical) stacking for incoherent noise suppression, strict quality control of sensor “trace” (recording of sensor amplitude with respect to time) data prior to data processing. A method of beam steering is disclosed to define the spatial response of the sensor array to sharply focus with higher lateral and vertical resolution at a particular 3D point in the Earth's subsurface using travel-times calculated in either time-migration or depth-migration domains, shading of the steered receiver beam to suppress the side-lobe pass-band for coherent interference. Multiple applications of the above method may be used at separated times to enable 4D imaging of the subsurface.
The current art of delay-filter-sum beamforming as disclosed in the '748 patent where filter coefficients are defined to modify (or shade) the side-lobe response of the sensor array, is well understood as belonging to the class of spectral-based algorithms for spatial-temporal (Wiener) filters. The determination of optimal filter coefficients may be performed according to a number of different algorithms; for example, constrained minimum least-mean-squares optimization using the Levinson algorithm. Alternative algorithms and application-specific filter designs are generally formulated as a constrained optimization problem with different choices of cost functions and constraints on the solutions. See, Kootsookos, P. J., Ward, D. B., Williamson, R. C., “Imposing pattern nulls on broadband array responses,” J. Acoust. Soc. Am., Vol. 105, No. 6, June 1999.
A general underlying requirement of Wiener filter theory is the mathematical existence of a solution, which requires that there exist a matrix of measured correlations between sensors for a sufficient range of space and/or time dimensions with a rank equal or greater than the number of filter coefficients being determined. Apart from a normalization constant, this matrix is also known in the art as a covariance matrix. For problems where the rank of this correlation matrix is less than the number of filter coefficients being sought, there is no solution. Despite the lack of a formal solution, it is sometimes proposed that a “generalized inverse” of the rank-deficient correlation matrix provides an optimal filter in a least-squares sense.
Another limitation of the present art of determining optimal filter coefficients lies in the lack of scalability of the solution methods. The time required to obtain a solution to the filter design problem scales as the cube of the number of filter coefficients using the direct covariance matrix inversion method. Iterative methods can be devised to avoid the direct inversion of the covariance matrix, but this only reduces the computational complexity to being proportional to the square of the number of filter coefficients. This again can prove prohibitively computationally costly for large sensor arrays with filter banks with large numbers of so-called “taps” (or coefficients).
Finally, the present art of delay-filter-sum beamforming as disclosed in the '748 patent of Guigné et al. does not address the mathematical and physical analysis of the acquired data set that can be applied prior to applying the filter-sum operation to generate the output image of that method. An exact decomposition of the acquired dataset using fundamental properties of physical and mathematical descriptions of the dataset can be exploited to isolate and selectively remove multiple sources of coherent interference. This capability is essential when the signals of interest are greatly diffused (e.g. non-specular returns) in relation to the dominant sources of coherent interference (e.g. specular returns and ground roll). In the hierarchy of beamforming methods, this approach can be termed a delay-classify-filter-sum beamforming method.